JP2007101279A - Correction coefficient determining method of rectangular coordinate moving mechanism, and collecting method of measuring data - Google Patents

Correction coefficient determining method of rectangular coordinate moving mechanism, and collecting method of measuring data Download PDF

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JP2007101279A
JP2007101279A JP2005289527A JP2005289527A JP2007101279A JP 2007101279 A JP2007101279 A JP 2007101279A JP 2005289527 A JP2005289527 A JP 2005289527A JP 2005289527 A JP2005289527 A JP 2005289527A JP 2007101279 A JP2007101279 A JP 2007101279A
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axis
correction coefficient
axes
measurement
length
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Takeshi Hagino
健 萩野
Makoto Abe
阿部　　誠
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Mitutoyo Corp
Mitsutoyo Kiko Co Ltd
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Mitsutoyo Kiko Co Ltd
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Abstract

<P>PROBLEM TO BE SOLVED: To estimate a correction coefficient of linearity and squareness of each axis with a small number of measurements in a lump. <P>SOLUTION: Regarding a total of seven directions of diagonal four directions and three axial directions of a rectangular parallelepiped specified by three axes XYZ, measuring value data M is obtained (S1) by measuring length using a length reference apparatus whose length is known. Error ε of each direction is determined based on the measuring data M (S2). The correction coefficients of the linearity of each axis and the squareness between respective axes are estimated using a least squares method based on the determined error of each direction (S3). <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

本発明は、直交三軸を運動軸とする直交座標運動機構の各軸のリニアリティおよび各軸間の直角度の補正係数を決定するための直交座標運動機構の補正係数決定方法および測定データの収集方法に関する。   The present invention relates to a method for determining a correction coefficient of a Cartesian coordinate motion mechanism and a collection of measurement data for determining the linearity of each axis of the Cartesian coordinate motion mechanism having three orthogonal axes as motion axes and the correction coefficient of the perpendicularity between the axes. Regarding the method.

三次元測定機のような三軸が直交した運動機構を持つ装置の運動誤差は、一軸当たり、リニアリティ、２方向の真直度、ピッチング、ヨーイング、ローリングの６個、さらに各軸間の直角度誤差３個の合計６×３＋３＝２１のパラメータで表される。このような直交座標運動機構において、高精度な運動機構を実現するためには、これらの運動誤差に対して数値補正を適用することが有効である。三次元測定機の場合は、レーザ干渉計やブロックゲージ、ステップゲージ等の長さ基準器、ストレートエッジ等を用いて、これらの運動誤差の補正パラメータを算出する。しかし、これらの補正パラメータを適用して数値補正を行っても、補正の残差が生じる場合には、数値補正された結果に加算して、さらに補正係数を適用する必要がある。この補正係数は、例えば各軸リニアリティのスケールファクタと、直角度誤差から求められる。   The motion error of a device with a motion mechanism in which three axes are orthogonal, such as a three-dimensional measuring machine, is 6 per axis, linearity, straightness in two directions, pitching, yawing and rolling, and squareness error between each axis. It is expressed by a total of 3 parameters of 6 × 3 + 3 = 21. In order to realize a highly accurate motion mechanism in such a Cartesian coordinate motion mechanism, it is effective to apply numerical correction to these motion errors. In the case of a three-dimensional measuring machine, these motion error correction parameters are calculated using a length reference device such as a laser interferometer, block gauge or step gauge, straight edge, or the like. However, even if numerical correction is performed by applying these correction parameters, if a correction residual is generated, it is necessary to add a correction coefficient to the result of the numerical correction and then apply the correction coefficient. This correction coefficient is obtained from, for example, the scale factor of each axis linearity and the squareness error.

一方、従来、三次元測定機の精度検査に三次元空間内の任意の方向に設置可能なブロックゲージ、ステップゲージ等を用いることが知られている（特許文献１）。しかし、この特許文献１には、補正係数の算出に際して、どのような測定を行うかの具体的手順は開示されていない。
実願昭６２−１５８３５８号のマイクロフィルム（実開平１−６４００４号）、第８頁〜第１３頁、第１図 On the other hand, conventionally, it is known to use a block gauge, a step gauge, or the like that can be installed in an arbitrary direction in a three-dimensional space for accuracy inspection of a three-dimensional measuring machine (Patent Document 1). However, this Patent Document 1 does not disclose a specific procedure for performing measurement when calculating the correction coefficient.
No. 62-158358, microfilm (Japanese Utility Model Application No. 1-64004), pages 8 to 13, FIG.

本発明は、各軸リニアリティと直角度の補正係数を、少ない測定回数で一括推定することを可能にする簡便な直交座標運動機構の補正係数決定方法及び測定データの収集方法を提供することを目的とする。   It is an object of the present invention to provide a simple orthogonal coordinate motion mechanism correction coefficient determination method and measurement data collection method that can collectively estimate the linearity and squareness correction coefficients for each axis with a small number of measurements. And

本発明に係る直交座標運動機構の補正係数決定方法は、互いに直交する三軸を運動軸とする運動機構の前記各軸のリニアリティおよび各軸間の直角度の補正係数を決定する補正係数決定方法において、前記三軸で規定される直方体の対角４方向及び前記三軸方向の計７方向について長さが既知である長さ基準器を用いた長さ測定を行って測定値データを取得するステップと、前記測定データから前記各方向についての誤差を求めるステップと、前記求められた各方向についての誤差から最小二乗法により前記各軸のリニアリティおよび各軸間の直角度の補正係数を一括推定するステップとを備えていることを特徴とする。   The correction coefficient determination method for the Cartesian coordinate motion mechanism according to the present invention is a correction coefficient determination method for determining the linearity of each axis of the motion mechanism having three axes orthogonal to each other as the motion axis and the correction coefficient of the perpendicularity between the axes. , The length measurement is performed using a length reference device having a known length in four diagonal directions of the rectangular parallelepiped defined by the three axes and a total of seven directions of the three axes, thereby obtaining measurement value data. A step of obtaining an error in each direction from the measurement data, and collectively estimating a linearity of each axis and a squareness correction coefficient between the axes by a least square method from the obtained error in each direction And a step of performing.

また、本発明に係る測定データの収集方法は、互いに直交する三軸を運動軸とする運動機構の前記各軸のリニアリティおよび各軸間の直角度の補正係数を一括推定するための測定データの収集方法であって、長さ基準器を、前記三軸で規定される直方体の対角４方向及び前記三軸方向の計７方向について配置して、前記運動機構を動作させて各方向について長さ測定を行うことにより各方向についての測定データを収集することを特徴とする。   In addition, the measurement data collection method according to the present invention includes measurement data for collectively estimating the linearity of each axis of the motion mechanism having three axes orthogonal to each other and the correction coefficient of the perpendicularity between the axes. In the collecting method, the length reference device is arranged in a total of 7 directions of 4 diagonal directions of the rectangular parallelepiped defined by the three axes and the three axis directions, and the movement mechanism is operated to increase the length in each direction. Measurement data for each direction is collected by measuring the length.

本発明の直交座標運動機構の補正係数決定方法によれば、三軸で規定される直方体の対角４方向及び前記三軸方向の計７方向について長さが既知である長さ基準器を用いた長さ測定を行って測定値データを取得し、この測定データから各方向についての誤差を求め、求められた各方向についての誤差から最小二乗法により前記各軸のリニアリティおよび各軸間の直角度の補正係数を一括推定するようにしているので、各軸リニアリティと直角度の補正係数を、少ない測定回数で一括推定することができる。   According to the correction coefficient determination method for the Cartesian coordinate motion mechanism of the present invention, a length reference device whose length is known in four diagonal directions of a rectangular parallelepiped defined by three axes and a total of seven directions of the three axes is used. Measurement data is obtained by measuring the measured length, and the error in each direction is obtained from this measurement data.The linearity of each axis and the straight line between each axis are obtained from the obtained error in each direction by the least square method. Since the angle correction coefficient is collectively estimated, the linearity of each axis and the square angle correction coefficient can be estimated collectively with a small number of measurements.

また、本発明の測定データ収集方法によれば、長さ基準器を、三軸で規定される直方体の対角４方向及び三軸方向の計７方向について配置して、運動機構を動作させて各方向について長さ測定を行うことにより各方向についての測定データを収集するようにしているので、各軸リニアリティと直角度の補正係数を推定するのに必要なデータを少ない測定回数で収集することが可能になる。一括推定することができる。   In addition, according to the measurement data collection method of the present invention, the length reference device is arranged in a total of 7 directions of 4 diagonal directions and 3 axis directions of a rectangular parallelepiped defined by 3 axes, and the motion mechanism is operated. Since the measurement data for each direction is collected by measuring the length in each direction, the data necessary to estimate the linearity of each axis and the correction factor of the squareness should be collected with a small number of measurements. Is possible. Batch estimation is possible.

以下、本発明の好ましい実施の形態について説明する。   Hereinafter, preferred embodiments of the present invention will be described.

［比較例］
先ず、本発明の一実施形態を説明するに当たり、比較例として直交座標系の各軸リニアリティと、各隣接軸間の直角度の補正係数をそれぞれ個別に算出する方法について説明する。なお、ここでは、一例としてステップゲージを測定することによって、補正係数を取得する方法について説明する。 [Comparative example]
First, in describing one embodiment of the present invention, as a comparative example, a method for individually calculating each axis linearity of an orthogonal coordinate system and a perpendicularity correction coefficient between adjacent axes will be described. Here, as an example, a method for obtaining a correction coefficient by measuring a step gauge will be described.

図４にステップゲージの概要を示す。ステップゲージ１０は棒状のベース１１の上にＮ個のブロック１２１，１２２，…，１２Ｎが１方向に一定間隔で配列されて固定されたもので、ベース１１の一端に設定された基準面Ｓから、各ブロック１２１〜１２Ｎの端面までの距離Ｌｉ（ｉ＝１，２，…，Ｎ）が校正された長さ基準器である。各ブロック端面までの距離の校正値ベクトルをＬ＝｛Ｌ１、Ｌ２、・・・、Ｌｎ｝とする。このステップゲージ１０を三次元測定機の測定空間内の任意方向に設置する。この状態で、プローブでＮ個のブロック１２１〜１２Ｎの端面位置を測定し、Ｎ個の測定値ベクトルＭ＝｛Ｍ１、Ｍ２、・・・Ｍｎ｝を得る。測定値Ｍと校正値Ｌの差を計算すれば、長さ測定の誤差ベクトルε＝｛ε１、ε１、ε２、・・・εｎ｝が得られる。例えばステップゲージ１０を三次元測定機のＹ軸に沿って設置した場合は、この測定長さに対応した誤差εの一次成分がＹ軸のリニアリティの補正係数となる。 FIG. 4 shows an outline of the step gauge. The step gauge 10 has N blocks 12 1 , 12 2 ,..., 12 N arranged on a bar-shaped base 11 and fixed in one direction at regular intervals, and is a reference set at one end of the base 11. This is a length reference device in which distances L i (i = 1, 2,..., N) from the surface S to the end surfaces of the blocks 12 1 to 12 N are calibrated. Let L = {L 1 , L 2 ,..., L n } be a calibration value vector for the distance to each block end face. The step gauge 10 is installed in an arbitrary direction within the measurement space of the coordinate measuring machine. In this state, the end face positions of the N blocks 12 1 to 12 N are measured by the probe, and N measurement value vectors M = {M 1 , M 2 ,... M n } are obtained. When the difference between the measured value M and the calibration value L is calculated, the length measurement error vector ε = {ε 1 , ε 1 , ε 2 ,... Ε n } is obtained. For example, when the step gauge 10 is installed along the Y-axis of the coordinate measuring machine, the primary component of the error ε corresponding to this measurement length is the Y-axis linearity correction coefficient.

各軸リニアリティの補正係数を算出するための測定において、ステップゲージ１０を三次元測定機の測定空間内に設置する位置を図５に示す。測定空間となる直方体Ｃにおいて、Ｘ軸の補正係数を取得する場合は［１］、Ｙ軸の補正係数を取得する場合は［２］、Ｚ軸の補正係数を取得する場合は［３］の位置にステップゲージを設置し、それぞれ長さ測定誤差列｛ε｝を求め、補正係数を算出する。   FIG. 5 shows a position where the step gauge 10 is installed in the measurement space of the coordinate measuring machine in the measurement for calculating the correction coefficient of each axis linearity. In the rectangular parallelepiped C serving as a measurement space, [1] is used to obtain the X-axis correction coefficient, [2] is obtained to obtain the Y-axis correction coefficient, and [3] is obtained to obtain the Z-axis correction coefficient. A step gauge is installed at the position, a length measurement error sequence {ε} is obtained for each, and a correction coefficient is calculated.

続いて、直角度の補正係数を算出するための測定の例として、Ｘ軸とＹ軸の直角度の補正係数を算出するための測定において、ステップゲージを三次元測定機の測定空間内に設置する位置を図６に示す。この例では測定空間である直方体Ｃの一面を形成するＸＹ平面内の対角線方向において、［４］と［５］に示す２組の測定を行う。校正値ベクトルＬと、２組の測定値ベクトルＭ［４］、Ｍ［５］とから求められる誤差ベクトルε［４］、ε［５］は、直角度誤差が存在する場合には一方が正方向、もう一方が負方向の誤差を生じる。ε［４］、ε［５］の差から、Ｘ軸とＹ軸の直角度の補正係数を算出することができる。すべての直角度の補正係数を算出するために、Ｘ軸とＺ軸の間、Ｙ軸とＺ軸の間、それぞれに対して同様の測定と補正係数の算出を行う。合計で６組の測定が必要である。 Subsequently, as an example of the measurement for calculating the squareness correction coefficient, a step gauge is installed in the measurement space of the coordinate measuring machine in the measurement for calculating the squareness correction coefficient of the X axis and the Y axis. The position to perform is shown in FIG. In this example, two sets of measurements shown in [4] and [5] are performed in the diagonal direction in the XY plane that forms one surface of the rectangular parallelepiped C that is the measurement space. The error vectors ε [4] and ε [5] obtained from the calibration value vector L and the two sets of measured value vectors M [4] and M [5] are positive when one of the squareness errors exists. An error occurs in the direction and the other direction in the negative direction. From the difference between ε [4] and ε [5] , the correction coefficient of the perpendicularity between the X axis and the Y axis can be calculated. In order to calculate all squareness correction coefficients, the same measurement and correction coefficient calculation are performed between the X axis and the Z axis, and between the Y axis and the Z axis, respectively. A total of 6 sets of measurements are required.

以上により、三軸が直交した運動機構を持つ装置の、リニアリティと直角度の補正係数を算出することができる。   As described above, the linearity and squareness correction coefficients of the apparatus having the motion mechanism in which the three axes are orthogonal can be calculated.

この方法の問題点として、ステップゲージ測定回数が多いことと、補正係数の算出が煩雑であることがあげられる。この方法では、各軸のリニアリティのために３回、直角度のために６回、合計で９回ステップゲージを測定する必要がある。また、はじめにＸ軸のリニアリティを測定して補正係数を算出し、続いてＹ軸及びＺ軸について同様に算出し、その後直角度の補正係数を算出する、といったように順次補正係数を算出していくので、手順が煩雑である。また、ひとつの補正係数を算出して数値補正に利用した後は、確認のための測定をその都度実行することが必須であり、さらに手順の煩雑化を生じさせる。   Problems of this method include a large number of step gauge measurements and a complicated calculation of the correction coefficient. In this method, it is necessary to measure the step gauge three times for linearity of each axis and six times for squareness, for a total of nine times. In addition, the correction coefficient is calculated sequentially by first measuring the linearity of the X axis and calculating the correction coefficient, then calculating similarly for the Y axis and the Z axis, and then calculating the correction coefficient for the squareness. The procedure is complicated. In addition, after calculating one correction coefficient and using it for numerical correction, it is essential to perform measurement for confirmation each time, which further complicates the procedure.

そこで本発明では、各軸リニアリティと直角度の補正係数を、７組の測定値から最小二乗法によって一括で推定する簡便な手法を提案する。   Therefore, the present invention proposes a simple method for collectively estimating the linearity and squareness correction coefficients for each axis from the seven sets of measured values by the least square method.

［実施形態１］
図１は、本発明の一実施形態に係る直交座標運動機構の補正係数決定方法を説明するための図で、直交座標運動機構として三次元測定機を、また長さ基準器としてステップゲージを用いた例を示す図である。 [Embodiment 1]
FIG. 1 is a diagram for explaining a correction coefficient determination method for a Cartesian coordinate motion mechanism according to an embodiment of the present invention. A coordinate measuring machine is used as a Cartesian coordinate motion mechanism, and a step gauge is used as a length reference device. FIG.

三次元測定機２０は、次のように構成されている。図示しないワークを載置する定盤２１の両側端からアーム支持体２２，２３が立設され、それらの上端でＸ軸ガイド２４が支持されている。アーム支持体２２は、その下端がＹ軸駆動機構２５によってＹ軸方向に駆動され、アーム支持体２３は、その下端がエアーベアリングによって定盤２１上にＹ軸方向に移動可能に支持されている。Ｘ軸ガイド２４は、垂直方向に延びるＺ軸ガイド２６をＸ軸方向に駆動する。Ｚ軸ガイド２６には、Ｚ軸アーム２７がＺ軸ガイド２６に沿って駆動されるように設けられ、Ｚ軸アーム２７の下端に接触式のプローブ２８が装着されている。このプローブ２８が定盤２１上に載置されたワークに接触したときに、プローブ２８からコントローラ３１にタッチ信号が出力され、そのときのＸＹＺ座標値をコントローラ３１が取り込むようになっている。コンピュータ３２は、コントローラ３１で取り込んだＸＹＺ座標値から後述する補正係数算出処理を実行する。   The three-dimensional measuring machine 20 is configured as follows. Arm supports 22 and 23 are erected from both side ends of a surface plate 21 on which a workpiece (not shown) is placed, and an X-axis guide 24 is supported at the upper ends thereof. The lower end of the arm support 22 is driven in the Y-axis direction by the Y-axis drive mechanism 25, and the lower end of the arm support 23 is supported on the surface plate 21 by the air bearing so as to be movable in the Y-axis direction. . The X-axis guide 24 drives a Z-axis guide 26 extending in the vertical direction in the X-axis direction. A Z-axis arm 27 is provided on the Z-axis guide 26 so as to be driven along the Z-axis guide 26, and a contact type probe 28 is attached to the lower end of the Z-axis arm 27. When the probe 28 comes into contact with the workpiece placed on the surface plate 21, a touch signal is output from the probe 28 to the controller 31, and the controller 31 takes in the XYZ coordinate values at that time. The computer 32 executes a correction coefficient calculation process described later from the XYZ coordinate values captured by the controller 31.

補正係数の決定に当たり定盤２１には、図４と同様のステップゲージ１０が載置される。このステップゲージ１０は、定盤２１に設置される支持機構４０に支持されている。支持機構４０は中心軸がＺ軸に沿った円柱状で、その下端が定盤２１に設置されるベース４１を形成し、上端がステップゲージ１０と連結される連結部４２を形成している。連結部４２は、ステップゲージ１０を、Ｚ軸（垂直方向）を回転軸として回転可能に、且つＺ軸と平行な任意の面内で回転可能に連結する。この構造により、ステップゲージ１０を三次元測定機２０の三次元測定空間に対して任意の方向に配置することが可能になる。   In determining the correction coefficient, the step gauge 10 similar to that shown in FIG. The step gauge 10 is supported by a support mechanism 40 installed on the surface plate 21. The support mechanism 40 has a cylindrical shape with a central axis along the Z axis, and a lower end thereof forms a base 41 installed on the surface plate 21, and an upper end thereof forms a connecting portion 42 connected to the step gauge 10. The connecting portion 42 connects the step gauge 10 so as to be rotatable about the Z axis (vertical direction) as a rotation axis and to be rotatable in an arbitrary plane parallel to the Z axis. With this structure, the step gauge 10 can be arranged in an arbitrary direction with respect to the three-dimensional measurement space of the three-dimensional measuring machine 20.

図２は、本実施形態における、コンピュータ３２で実行される各軸のリニアリティと各軸間の直角度の補正係数を最小二乗法により一括推定する処理を示すフローチャート、図３は上記処理に必要なステップゲージ１０の配置方向を示す図である。   FIG. 2 is a flowchart showing a process for collectively estimating the linearity of each axis and the correction coefficient of the squareness between each axis, which is executed by the computer 32, and FIG. 3 is necessary for the above process. It is a figure which shows the arrangement | positioning direction of the step gauge.

ステップゲージ１０は、図３に示すように、三次元測定機２０の測定空間を示す直方体Ｃの対角方向［１］〜［４］と、Ｘ軸、Ｙ軸、Ｚ軸の各軸に沿った方向［５］〜［７］の、合計７つの方向に配置する。そして、各方向について長さ測定を行う（Ｓ１）。いま、［１］の方向に配置されたステップゲージ１０を三次元測定機２０で測定することにより得られた測定値ベクトルをＭ１，同じく［２］の方向の測定値ベクトルをＭ２，…，［７］の方向の測定値ベクトルをＭ７とすると、これらの測定により、以下に示すＭ１〜Ｍ７の計７組の測定値ベクトルを得ることができる（Ｓ１）。 As shown in FIG. 3, the step gauge 10 is along the diagonal directions [1] to [4] of the rectangular parallelepiped C indicating the measurement space of the coordinate measuring machine 20 and the X axis, Y axis, and Z axis. It is arranged in a total of seven directions [5] to [7]. And length measurement is performed about each direction (S1). Now, the measured value vector obtained by measuring the step gauge 10 arranged in the direction [1] with the coordinate measuring machine 20 is M 1 , the measured value vector in the direction [2] is M 2 ,. , when M 7 a measurement vector in the direction of [7], these measurements can be obtained a total of 7 sets of measurement vector of M 1 ~M 7 below (S1).

Figure 2007101279
Ｍ１１は、測定方向［１］における１番目のブロック１２１の端面からの距離の測定値を示す。ここで、ｎ１，ｎ２，・・・ｎ７は、［１］〜［７］の測定のそれぞれの測定値の個数である。三次元測定機のような直交座標機構は、それぞれの軸に運動範囲が異なる場合がある。また対角方向は、各軸に沿った方向よりも運動範囲が大きい。このように、ステップゲージ１０を測定するような場合には、必ずしも測定可能なデータの個数は一致しない。
Figure 2007101279
 M 11 indicates a measured value of the distance from the end face of the first block 121 in the measurement direction [1]. Here, n1, n2,..., N7 are the numbers of measured values of the measurements [1] to [7]. An orthogonal coordinate mechanism such as a three-dimensional measuring machine may have a different range of motion for each axis. The diagonal direction has a greater range of motion than the direction along each axis. Thus, when the step gauge 10 is measured, the number of measurable data does not necessarily match.

次に、７組の測定値ベクトルＭ１〜Ｍ７と、各ブロック端面までの距離の校正値ベクトルＬ＝｛Ｌ１、Ｌ２、・・・、Ｌｎ｝との差から、以下に示す７組の誤差ベクトルε１〜ε７を得る（Ｓ２）。 Next, from the difference between the seven measurement value vectors M 1 to M 7 and the calibration value vector L = {L 1 , L 2 ,..., L n } of the distance to each block end face, the following is shown. Seven sets of error vectors ε 1 to ε 7 are obtained (S2).

Figure 2007101279
７組の誤差ベクトルを組み合わせて、測定値全体の誤差ベクトルを以下のように定義する。
Figure 2007101279
 By combining seven sets of error vectors, the error vector of the entire measurement value is defined as follows.

Figure 2007101279
続いて、未知の補正係数ベクトルを以下のように定義する。
Figure 2007101279
 Subsequently, an unknown correction coefficient vector is defined as follows.

Figure 2007101279
ここで、
αｘｙ，αｘｚ，αｙｚ：直角度の補正係数
αｘ，αｙ，αｚ：各軸のリニアリティの補正係数
α０１，α０２，…，α０７：［１］〜［７］の測定の誤差の０次成分
である。
Figure 2007101279
 here,
α xy , α xz , α yz : Squareness correction coefficient α x , α y , α z : Linearity correction coefficient for each axis α 01 , α 02 ,..., α 07 : Measurement of [1] to [7] This is the zero-order component of the error.

本方法では、αｘｙ，αｘｚ，αｙｚと、αｘ，αｙ，αｚと、合計６つの補正係数を一括推定することが目的である。この補正係数は、誤差ベクトルの１次成分で決定される。０次成分は補正係数の算出には必要ないので、α０１，α０２，…，α０７に分離する。 The purpose of this method is to collectively estimate a total of six correction factors, α xy , α xz , α yz , α x , α y , α z . This correction coefficient is determined by the primary component of the error vector. Since the zero-order component is not necessary for calculating the correction coefficient, it is separated into α 01 , α 02 ,..., Α 07 .

誤差ベクトルεと補正係数ベクトルαは、係数行列Ｙを仲介として次式の関係にある。   The error vector ε and the correction coefficient vector α have the following relationship with the coefficient matrix Y as an intermediary.

Figure 2007101279
数５の詳細は以下のようになる。
Figure 2007101279
 The details of Equation 5 are as follows.

Figure 2007101279
Figure 2007101279

ここで、［１］の１番目の測定点の座標値をＸ１１＝｛ｘ１１，ｙ１１，ｚ１１｝、測定の方向ベクトルをａ１１＝｛ａｉ１１，ａｊ１１，ａｋ１１｝とすると、数６中の［Ｙｘｙ１１ Ｙｘｚ１１ Ｙｙｚ１１］は、Ｘ１１とａ１１の外積誤差成分を示す係数であり、［Ｙｘ１１ Ｙｙ１１ Ｙｚ１１］は、Ｘ１１とａ１１の内積誤差成分を示す係数である。
数６から、最小二乗法の正規方程式は次式のように与えられる。 Here, [1] the coordinate values of the first measurement point X 11 = {x 11, y 11, z 11}, when the direction vector of the measurement and a 11 = {a i11, a j11, a k11} , in a few 6 [Y xy11 Y xz11 Y yz11 ] is a coefficient indicating a cross product error component of X 11 and a 11, the [Y x11 Y y11 Y z11] is the inner product error component of X 11 and a 11 It is a coefficient shown.
From Equation 6, the normal equation for the least squares method is given by the following equation.

Figure 2007101279
数７から、未知の補正係数ベクトルαは次式のように求められる（Ｓ３）。
Figure 2007101279
 From Equation 7, an unknown correction coefficient vector α is obtained as follows (S3).

Figure 2007101279
以上により、各軸のリニアリティと各軸間の直角度の補正係数を最小二乗法により一括推定することが可能である。
Figure 2007101279
 As described above, it is possible to collectively estimate the linearity of each axis and the correction coefficient of the squareness between each axis by the least square method.

［実施形態２］
最小二乗法を用いて補正係数を一括推定する場合に、［１］〜［７］のそれぞそれの測定において測定点数が異なった場合には、点数の多い測定結果の重みが増し、一括推定した結果に不具合を生じる場合がある。その場合は、重み係数行列Ｗを適切に選択し、数７を次式のように変更すれば、測定点数の違いに対してロバストに一括推定することが可能になる。 [Embodiment 2]
When the correction coefficient is collectively estimated using the least square method, if the number of measurement points is different in each measurement of [1] to [7], the weight of the measurement result having a large number of points is increased, and the batch estimation is performed. In some cases, the result may be defective. In that case, if the weighting coefficient matrix W is appropriately selected and Equation 7 is changed as shown in the following equation, it is possible to perform robust estimation against the difference in the number of measurement points.

Figure 2007101279
なお、以上の説明では、長さ基準器としてステップゲージを用いた測定方法について説明した。しかし、長さ基準器は、ブロックゲージやレーザ干渉計を用いる場合など、参照値となる長さが得られるものであればどのようなものでもよい。
Figure 2007101279
 In the above description, the measurement method using the step gauge as the length reference device has been described. However, the length standard device may be any device as long as a length serving as a reference value can be obtained, such as when a block gauge or a laser interferometer is used.

本発明により、各軸リニアリティと直角度の補正係数を、７組の測定値から一括で推定する簡便な手法を提案することができる。すなわち、比較例の方法では測定回数が９回必要であったのに対し、本発明では７回で良いので、校正作業の高速化が可能である。また、補正係数の算出は１回行えばよいので、手順の簡略化も実現できる。   According to the present invention, it is possible to propose a simple method for collectively estimating the linearity and the squareness correction coefficient from seven sets of measured values. That is, in the method of the comparative example, the number of times of measurement is 9 times, whereas in the present invention, 7 times is sufficient, so that the speed of the calibration work can be increased. Further, since the correction coefficient needs to be calculated only once, the procedure can be simplified.

この発明の一実施形態に係る補正係数推定方法を実現するための三次元測定機とこの測定機にセットされたステップゲージとを示す斜視図である。It is a perspective view which shows the three-dimensional measuring machine for implement | achieving the correction coefficient estimation method which concerns on one Embodiment of this invention, and the step gauge set to this measuring machine. 同三次元測定機におけるコンピュータで実行される補正係数推定方法を示すフローチャートである。It is a flowchart which shows the correction coefficient estimation method performed with the computer in the coordinate measuring machine. 同方法を実現するための三次元測定空間内におけるステップゲージの配置位置を示す斜視図である。It is a perspective view which shows the arrangement position of the step gauge in the three-dimensional measurement space for implement | achieving the same method. 長さ基準器としてのステップゲージを示す斜視図である。It is a perspective view which shows the step gauge as a length reference | standard device. 比較例における三軸方向の各軸リニアリティの補正係数を算出するためのステップゲージの配置位置を示す斜視図である。It is a perspective view which shows the arrangement position of the step gauge for calculating the correction coefficient of each axis | shaft linearity of a triaxial direction in a comparative example. 比較例における直角度の補正係数を算出するためのステップゲージの配置位置を示す斜視図である。It is a perspective view which shows the arrangement position of the step gauge for calculating the correction coefficient of the squareness in a comparative example.

符号の説明Explanation of symbols

１０…ステップゲージ、２０…三次元測定機、３１…コントローラ、３２…コンピュータ、４０…支持機構。   DESCRIPTION OF SYMBOLS 10 ... Step gauge, 20 ... CMM, 31 ... Controller, 32 ... Computer, 40 ... Support mechanism.

Claims (3)

互いに直交する三軸を運動軸とする運動機構の前記各軸のリニアリティおよび各軸間の直角度の補正係数を決定する直交座標運動機構の補正係数決定方法において、
前記三軸で規定される直方体の対角４方向及び前記三軸方向の計７方向について長さが既知である長さ基準器を用いた長さ測定を行って測定値データを取得するステップと、
前記測定データから前記各方向についての誤差を求めるステップと、
前記求められた各方向についての誤差から最小二乗法により前記各軸のリニアリティおよび各軸間の直角度の補正係数を一括推定するステップと
を備えたことを特徴とする直交座標運動機構の補正係数決定方法。 In the orthogonal coefficient motion mechanism correction coefficient determination method for determining the linearity of each axis of the motion mechanism having three motion axes orthogonal to each other and the perpendicularity correction coefficient between the axes,
Obtaining measurement data by performing length measurement using a length reference device having a known length in four diagonal directions of the rectangular parallelepiped defined by the three axes and a total of seven directions of the three axes; ,
Obtaining an error for each direction from the measurement data;
And a step of collectively estimating linearity of each axis and a correction coefficient of perpendicularity between each axis by a least-squares method from an error in each direction obtained. Decision method. 前記補正係数を一括推定するステップは、前記測定値データの個数が各方向の長さ測定毎に異なる場合、前記各方向についての誤差から重み付き最小二乗法により前記補正係数を求めるステップである
ことを特徴とする請求項１記載の直交座標運動機構の補正係数決定方法。 The step of collectively estimating the correction coefficient is a step of obtaining the correction coefficient by a weighted least square method from an error in each direction when the number of the measurement value data is different for each length measurement in each direction. The correction coefficient determination method for the Cartesian coordinate motion mechanism according to claim 1. 互いに直交する三軸を運動軸とする運動機構の前記各軸のリニアリティおよび各軸間の直角度の補正係数を一括推定するための測定データの収集方法であって、
長さ基準器を、前記三軸で規定される直方体の対角４方向及び前記三軸方向の計７方向について配置して、前記運動機構を動作させて各方向について長さ測定を行うことにより各方向についての測定データを収集する
ことを特徴とする測定データの収集方法。 A method of collecting measurement data for collectively estimating linearity of each axis of a motion mechanism having three axes orthogonal to each other as a motion axis and a correction factor of perpendicularity between each axis,
By arranging length reference devices in a total of 7 directions including the diagonal 4 directions of the rectangular parallelepiped defined by the three axes and the three axes, the length is measured in each direction by operating the motion mechanism. A method for collecting measurement data, characterized by collecting measurement data for each direction.
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